On Aug 26, 6:21 am, "Nicolas M. Thiery" <nicolas.thi...@u-psud.fr> wrote: > Dear and Javier, dear John,
[snip] > So in the long run, we definitely need both the direct sum and the > direct product functorial constructions, with appropriate > "inheritance" to share whatever is valid for both direct products and > direct sums. For the moment, I'll just leave a note about this in the > code (for the moment, this feature is essentially used nowhere). > > A little question: if V and W are two vector spaces which turn out to > be also in stronger categories, some with direct sums, and some > without, what should the following do: > > sage: direct_sum(V, W) Could there be an optional argument: sage: direct_sum(V, W, cat) If cat is not present, find the "strongest" category which contains both V and W, and compute the direct sum there, raising an error if it doesn't exist. (Or just raise an error? Or raise an error, saying what this strongest category is, and suggesting computing the direct sum there? Maybe I like this last approach the best.) If cat is present, check that cat contains both V and W, and then compute the direct sum there. > One 100% safe option is to raise an error. > > Another would be to return the direct sum (as vector spaces) of V and > W, which is also a direct product (that would be another story if the > sum was infinite), and to endow it with whatever operations from the > other categories applying either to direct sums or to direct products. This approach doesn't make sense to me: V and W can also be viewed as sets, but their coproduct as sets is not the same as their coproduct as vector spaces. Why choose one over the other? And what if there is a third category (like commutative k-algebras) in which the coproduct is again different (like the tensor product)? John --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To post to this group, send email to sage-combinat-devel@googlegroups.com To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en -~----------~----~----~----~------~----~------~--~---
